Simple tensor products

By D. Hernandez. 2009

56 citations recorded by the source corpus.

Let ℱ be the category of finite-dimensional representations of an arbitrary quantum affine algebra. We prove that a tensor product S1⊗⋅⋅⋅⊗SN of simple objects of ℱ is simple if and only Si⊗Sj is simple for any i

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8f70afd08019aa3037bac5b8a8ae5c880d1153fb

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Citations in the corpus

BAXTER'S RELATIONS AND SPECTRA OF QUANTUM INTEGRABLE MODELS (2013, unknown): “ rδ−α1x − 1,0 +φ − 1,−rk1. 28 EDWARD FRENKEL AND DAVID HERNANDEZ 6.6. Tensor product of ℓ-weight vectors. By using (6.22), we prove exactly as in [H4, Proposition 3.2] the following. Proposition 6.9. [H4] Let V1,V2 in category Oand consider an l-weight vector w = X α wα ⊗vα ! + X β w′ β ⊗v ′ β ∈ ”
Quantum Grothendieck rings and derived Hall algebras (2011, background): “∈vZB∗if and only if χeq,t(L1)∗···∗χeq,t(Lk)is the (q,t)-character of a simple module up to a power ofv, that is by Corollary 5.5, if and only if L1 ⊗···⊗Lk is simple. Hence Corollary 1.4 follows from [He4]. 7 A presentation of quantum Grothendieck rings In the remaining sections we drop the symbol ∗”
Representations of Algebras and Related Topics (2011, background): “an of subrepresentations of M[β] with dimension vector ν. Let αand Yα be related to βas in Eq.(25), (26). Finally, recall the notation vi := A−1 i,qξi+1. 6This theorem was later extended by Hernandez [23] to the whole category C. 28 Bernard Leclerc W 2(3) α2(3) W 1(2) α1(2) V 2(2) vnvnnB21(2) nnnnn ”
Tensor diagrams and cluster algebras (2012, background): “ inspired by the “ﬂag property” of cluster complexes (conjectural, but proved in many instances, see [14, Conjecture 5.5, Theorem 5.6]), and by the analogous property of the dual canonical basis (cf. [27], [40, Corollary 1.4]). We anticipate that all of the above conjectures generalize broadly. Our ”
Asymptotic representations and Drinfeld rational fractions (2011, background): “t;l) −→ L(M). Consider the linear subspace L(M)≥l = M m∈MZ[A−1 i,qr+di ]i∈I,r≥l (L(M))m . The following result will play a key role in subsequent sections. ASYMPTOTIC REPRESENTATIONS 15 Theorem 3.15. [H4] (i) The map (3.21) restricts to an isomorphism of vector spaces (3.22) L(M≥l)⊗v<l −→ L(M)≥l,”